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Colloquially speaking, image generation models based upon diffusion processes are frequently said to exhibit "hallucinations," samples that could never occur in the training data. But where do such hallucinations come from? In this paper,…

Diffusion based generative models have achieved unprecedented fidelity in synthesizing high dimensional data, yet the theoretical mechanisms governing multimodal generation remain poorly understood. Here, we present a theoretical framework…

Diffusion models, which convert noise into new data instances by learning to reverse a Markov diffusion process, have become a cornerstone in contemporary generative modeling. While their practical power has now been widely recognized, the…

Diffusion Probabilistic Models have demonstrated remarkable performance across a wide range of generative tasks. However, we have observed that these models often suffer from a Signal-to-Noise Ratio-timestep (SNR-t) bias. This bias refers…

Though diffusion-based video generation has witnessed rapid progress, the inference results of existing models still exhibit unsatisfactory temporal consistency and unnatural dynamics. In this paper, we delve deep into the noise…

Diffusion models (DMs) have rapidly emerged as a powerful framework for image generation and restoration. However, existing DMs are primarily trained in a supervised manner by using a large corpus of clean images. This reliance on clean…

Denoising diffusion models have emerged as a powerful tool for various image generation and editing tasks, facilitating the synthesis of visual content in an unconditional or input-conditional manner. The core idea behind them is learning…

Spatiotemporal patterns are common in biological systems. For electrically-coupled cells previous studies of pattern formation have mainly used external forcing as the main bifurcation parameter. The purpose of this paper is to show that…

We have studied the entropy-driven mechanism leading to stationary patterns formation in stochastic systems with local dynamics and non-Fickian diffusion. We have shown that a multiplicative noise fulfilling a fluctuation-dissipation…

Empirical studies suggest that machine learning models often rely on features, such as the background, that may be spuriously correlated with the label only during training time, resulting in poor accuracy during test-time. In this work, we…

Out-of-distribution detection is crucial to the safe deployment of machine learning systems. Currently, unsupervised out-of-distribution detection is dominated by generative-based approaches that make use of estimates of the likelihood or…

Consistency models have recently been introduced to accelerate sampling from diffusion models by directly predicting the solution (i.e., data) of the probability flow ODE (PF ODE) from initial noise. However, the training of consistency…

Score-based diffusion models generate new samples by learning the score function associated with a diffusion process. While the effectiveness of these models can be theoretically explained using differential equations related to the…

Denoising diffusion models are a class of generative models which have recently achieved state-of-the-art results across many domains. Gradual noise is added to the data using a diffusion process, which transforms the data distribution into…

Most existing theoretical investigations of the accuracy of diffusion models, albeit significant, assume the score function has been approximated to a certain accuracy, and then use this a priori bound to control the error of generation.…

Diffusion models represent a class of generative models that produce data by denoising a sample corrupted by white noise. Despite the success of diffusion models in computer vision, audio synthesis, and point cloud generation, so far they…

We explore the connection between deep learning and information theory through the paradigm of diffusion models. A diffusion model converts noise into structured data by reinstating, imperfectly, information that is erased when data was…

We develop a microscopic transport theory in a randomly driven fermionic model with and without linear potential. The operator dynamics arise from the competition between noisy and static couplings, leading to diffusion regardless of…

While diffusion models can successfully generate data and make predictions, they are predominantly designed for static images. We propose an approach for efficiently training diffusion models for probabilistic spatiotemporal forecasting,…

We consider driven many-particle models which have a phase transition between an active and an absorbing phase. Like previously studied models, we have particle conservation, but here we introduce an additional symmetry - when two particles…